Problem: Simplify the following expression: $ t = \dfrac{10}{7} - \dfrac{4y + 6}{9y} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9y}{9y}$ $ \dfrac{10}{7} \times \dfrac{9y}{9y} = \dfrac{90y}{63y} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{4y + 6}{9y} \times \dfrac{7}{7} = \dfrac{28y + 42}{63y} $ Therefore $ t = \dfrac{90y}{63y} - \dfrac{28y + 42}{63y} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{90y - (28y + 42) }{63y} $ Distribute the negative sign: $t = \dfrac{90y - 28y - 42}{63y}$ $t = \dfrac{62y - 42}{63y}$